J.P. Morgan Chase & Co. is in discussions with U.S. electricity regulators about paying what would be a record fine to settle allegations that the bank manipulated electricity markets in California and the Midwest, according to people familiar with the talks.

The Federal Energy Regulatory Commission and the New York bank are exchanging drafts of an agreement that would result in J.P. Morgan paying hundreds of millions of dollars, these people said. The fine, they said, likely will be larger than the record $435...